Question

From past experience, a stockbroker believes that under present economic conditions a customer will invest in tax-free bonds with a probability of 0.6, will invest in mutual funds with a probability of 0.3, and will invest in both tax-free bonds and mutual funds with a probability of 0.15. At this time, find the probability that a customer will invest:

(a) in either tax-free bonds or mutual funds;
(b) in neither tax-free bonds nor mutual funds.

Answer 1

Answer:

A. 0.75

B. 0.25

Explanation:

Let : P(B) be probability of investing in tax free bonds, P(M) be probability of investing in mutual funds.

P (B or M) i.e P (B U M) = P(B) + P(M) + P (M ∩ B) i.e P (M & B)

P (B U M) = 0.6 + 0.3 - 0.15  

P (B U M) = 0.75

P (Neither B or M) = 1 - [ P ( B or M) ] = 1 - [ P ( B U M) ]

1 - 0.75 = 0.25